ducttapecrown

You got nothing wrong. To expand, you can add points on elliptic curves together. To add P and Q, you draw the line between them, find the third point on the line, and reflect it over the x-axis [1]. Then the idea is to find a generating set S of points so that every rational point on the elliptic curve is a sum of points from S. The size of S is called the rank of the elliptic curve.

[1] There are some details: https://en.wikipedia.org/wiki/Elliptic_curve#Group_law

I feel like LLM's will change advertising like internet search changed advertising.

Here "like" means similarly in magnitude, not direction. If I could predict the future etc.

It is not the technology that sucks ever more money out of the populace, it's the people at the top!

NYTimes competing with NYTimesPitchBot for funnier headlines, I see. What a bizarre and awesome piece of science. I like crystals for the miracle of uncountable numbers of atoms transferring symmetry from the smallest scale to the visible scale.

It's mentioned in the article that the chimpanzees only relinquished the crystals in exchange for many bananas, so it seems they're more into crystals...

This is just a general pattern: applied mathematicians are often using things pure mathematicians haven't proved to be true yet. The examples are widespread for the generalized Riemann hypothesis. There are statements we aren't sure about, but there's also a lot that we are sure about but not sure about the proof of.

Can you list some better books for those of us who liked Le Guin and are interested in what could be better?

The dots need to be the vertices of equilateral triangles for the Voronoi diagram to be hexagons, the above is a rectangular grid rotated 45 degrees.

You can overlay a regular hexagonal tessellation over a regular triangular tessellation to see this.

Location: Seattle

Remote: US time zones

Willing to relocate: to SF

Technologies: math, English, Python

Resume/CV: https://drive.google.com/file/d/1YlO2X6hwkPyf-CkdWparf7Tfle_...

Email: samdeclanla {at} gmail.com

Mathematician, want to work on AI. You only need to double my salary as a Ph.D. student and I'm on board lol.

Why is the scrolling janky?

Terry Tao is writing about this on his blog.

The bull case is that everyone losing their jobs will accelerate and bring about the socialist revolution, giving us universal basic income and universal healthcare.

How long did it take for mobile repair shops to proliferate? Surely solar repair shops will also appear.

It reads more like mysticism than a serious claim of novelty, chill out.

Lee taught Intro to Topological Manifolds for one quarter, and then the next two quarters where Intro to Smooth Manifolds. Then Riemannian, then vector bundles, and then complex manifolds.

Location: Seattle Remote: US time zones Willing to relocate: to SF Technologies: math, English, Python Resume/CV: https://drive.google.com/file/d/1YlO2X6hwkPyf-CkdWparf7Tfle_... Email: samdeclanla {at} gmail.com

Mathematician, want to work on AI. You only need to double my salary as a Ph.D. student and I'm on board lol.

Yesterday there was an article about how the ear works more like a Gabor transform or a wavelet transform than a Fourier transform, both of which are Short Time Fourier Transforms, so yes!

We need investors to fund ideas to find out if they are good or bad. It is called testing.

A function (which is an isomorphism) from complex numbers a+bi to matrices is a+bi |-> [[a,-b],[b,a]] where the matrix is listed by rows. So i is sent to the matrix R with a 0 in the top left, 1 in the bottom left, 0 in the bottom right and a -1 in the top right. R is a 90 degree rotation, you can check that it sends the unit vector [1,0] on the x-axis to [0,1], and the unit vector [0,1] on the y-axis to [-1,0].

It turns out incremental thought is much better than original thought. I guess.

Doctors would implement self-healing and abolish checklists if they could! Be glad if you don't need a checklist.

Depends on if the managers above them are accountable or not. Accountability is the opposite of corruption and both need to come from the top.

Is the LHC humanity's biggest let down? Confirmed the existence of the Higgs boson but birthed 0 black holes!

Here, I asked ChatGPT to summarize it for you:

just kidding.

How did you pick the number "about a dozen"? Probably just LLM budget constraint I guess.

You could make an analogous course titled "Mathematics for [subfield of mathematics]" for any subfield of math. It would be a good(ish) title (I have never titled a course), and the content would be nicely focused.

Such courses are generally titled "Intro to".

The mathematician in question doesn't believe in infinity as an axiom, so he has a different understanding of what finding irrational roots means than others. From what I've gleaned from the other comments, it sounds like he does use an iterative algorithm to produce a power series solution.

Geometry only benefits from visual reasoning in 3d and lower, and there are a lot of dimensions above that!

You can see visual reasoning as a little cheat computation, you can run math problems through your sense-determining brain, which is what brains are really good at (robots struggle with our levels of dexterity). But the fact remains that you can only visualize in low dimensions, and there are infinitely many dimensions.

Note: You can reduce many problems to 3d, but also many problems in 3d have configuration spaces with much higher dimension, so there's some nuance.

They get it from being an engineer!

Since it says "linked", there may be exceptions, every body is different.